The Curvature of spacetime?? how?

[maddog]

DanielFB,

Between Qfwfq and UncleAl I feel answered adequately your first post. However
the one below needs a bit more.

Originally Posted by DanielFB

this sounds good, but however, I regret to say that if space is now physical it can no longer be space. I like to think of it in terms of a football field and it's boundaries. Now, it matters not how many players there are in the field, the boundaries never increase. What happens is new. The players fill over the edges, but the boundaries remain really fixed into reality. The same applies to space. But if general relaitivity is right, space must now be thought of as a mental construct, and nothing physical, say.

I have reread this a few times and am now not sure of your position.

Space is "physical" or not. [may you meant to not for now]

The space we live in is only a metric (like the boundries in your example) or
a measure. Whenever we represent a system by some graph or picture, it
is always a mental construct (GR or otherwise). We define a set of
coordinates and scale to assist with our graph and orient it appropriately.
It maybe you are not aware of Differential Geometry as Qfwfq mention or
considering other forms of Geometry than that of Euclid as UncleAl said.
Non-Euclidian geometry has been with us since about the 1850s or so. It is
true it was not fully utilized in physics until General Relativity. This is the
modern view today though.

Do a google search on "Differential Geometry" or "Noneuclidian geometry",
goto Wolfrom website or Mathworld or something. Learning new things is
good.

maddog

[Karnuvap]

The way that I imagine 'curved space' is to take a rubber eraser - one of those large rectangular ones. The grab it and twist it. Hold the resulting shape in mind and now mentally remove the rubber. What you have left is the curved vacuum of a non-euclidean space time.

Or imagine a large box containing jelly. The jelly contains a regular rectilinear array of those sugar pearls. Take the box away so you just have the jelly. Squeeze it between your palms so that the blob of jelly is no longer rectangular. Finally take away the jelly and the twisted array of sugar pearls represents twisted space but only if you take away the sugar pearls as well leaving behind a vacuum which is curved spacetime.